In this paper, we prove that every F ∗ space (i.e., Hausdorff topological vector space satisfying the first countable axiom) can be characterized by means of its “standard generating family of pseudo-norms”. By using the standard generating family of pseudo-norms P, the concepts of P-bounded set and γ-maxpseudo-norm-subadditive operator in F ∗ space are introduced. The uniform boundedness princ...

A Mathematical model has been considered to study the reflection and refraction phenomenon of plane wave at the interface of an isotropic liquid medium and a triclinic (anisotropic) half-space. The incident plane qP wave generates three types of reflected waves namely quasi-P (qP), quasi-SV (qSV) and quasi-SH (qSH) waves in the tric...

We investigate some basic descriptive set theory for countably based completely quasi-metrizable topological spaces, which we refer to as quasi-Polish spaces. These spaces naturally generalize much of the classical descriptive set theory of Polish spaces to the non-Hausdorff setting. We show that a subspace of a quasi-Polish space is quasi-Polish if and only if it is Π2 in the Borel hierarchy. ...

We give necessary and sufficient conditions for the Hardy operator to be bounded on a rearrangement invariant quasi-Banach space in terms of its Boyd indices. MAIN RESULTS A rearrangement invariant space X on R is a set of measurable functions (modulo functions equal almost everywhere) with a complete quasi-norm ‖ · ‖X such that the following holds: i) if g ≤ f ∗ and f ∈ X, then g ∈ X with ‖g‖X...

A quasi-metric is a distance function which satisfies the triangle inequality but is not symmetric: it can be thought of as an asymmetric metric. Quasi-metrics were first introduced in 1930s and are a subject of intensive research in the context of topology and theoretical computer science. The central result of this thesis, developed in Chapter 3, is that a natural correspondence exists betwee...